The Improved Isometric Feature Mapping Algorithm With Its Application

When doing scientific research in the information age, we willinevitably encounter with a lot of high-dimensional data, which requiresus to process high-dimensional data. Dimension reduction algorithm is animportant technique to deal with high-dimensional data, it is also theimportant way to extract feature.The main purpose of dimensionreduction is to keep the internal geometric structure of the original data,and then map the original data into low dimensional Euclidean space.Thus the redundant information of the original data will be removed andprocessing data becomes more efficient and more convenient.The linear dimensionality reduction algorithms are based onsubstantial mathematical foundation,but the linear essence of thesealgorithms can’t show complex nonlinear manifold structure. So thenonlinear manifold learning algorithms such as ISOMAP(IsometricFeature Mapping),LLE(Locally Linear Embedding),LE(LaplacianEigenmap) and etc. come into being.This paper mainly analyses the isometric feature mapping algorithm,and discusses its improved algorithm. After that we apply it to projects.The main works in this paper are following:1. Analysing and researching the ISOMAP algorithm and the kernelISOMAP algorithm. The conventional kernel ISOMAPalgorithm(K-ISOMAP) can not work well in keeping the intrinsictopology of datasets from multi-class clusters datasets in thelow-dimensional space. So applying the method of constructingneighborhood graph in MCMM-ISOMAP to the K-ISOMAP, and kernelmulti-class multi-manifold ISOMAP(K-MCMM-ISOMAP) will begot.This metod doesn’t only discover intrinsic topology of data inlow-dimensional mapping space, but also can directly map the new testdata from high-dimensional space to low-dimensional space. Therefore itcan be applied into the image retrieval system which consisting ofmulti-class image dataset.2. Aiming at the nonlinear and time series in production process of chemical industry, the paper applies a nonlinear fault diagnosis method tothe fault diagnosis of chemical process. It is constructed by thecombination of K-ISOMAP,LDA and KNN.Using K-ISOMAP to reducethe dimension firstly, it can keep the internal geometric structure of thetraining data. Then using LDA to maintain the best classification resultswhich is the feature extraction in process.Finally,classifying the resultwhich uses KNN algorithm. The results show that the fault diagnosismethod has high recognition ability.